Implications of the Game of Life

In 1970 a British mathematician, John Conway, devised a simple set of rules which simulates cellular life, often referred to as Conway’s Game of Life. In the Game of Life, the universe is a two-dimensional grid, with each cell obeying the following four simple rules, and coloured black if “alive” and white if “dead”.

Playing the Game

The rules are as follows

  1. Any live cell with fewer than two live neighbours dies, as if by underpopulation.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by overpopulation.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
Animation of Conway’s Game of Life

What is so remarkable about this is the demonstration that complexity can emerge from simple rules. Here are some isolated examples of simulated life-forms which can emerge from within the game:

Beyond the Game

What is very interesting is that if you change some of the properties of the rules, for example deciding that death by overpopulation can occur with only three neighbours rather than four, suddenly the nature of the universe changes. With most combinations of rules that you can try, life does not exist, and with a few one notices that quite different types of “life” starts to emerge.

Then if one experiments with different starting conditions, similar consequences are noticed. For example, if you start with the universe completely blank, then no life emerges, yet if you start with the universe 100% full of life, then all life immediately dies from overpopulation. Again, if the universe contains life, but it is too sparsely populated, then the cells immediately die in the next generation.  When you then gradually increase the population of the universe, it starts to become evident that at certain capacities life might exist for a few generations, it is not necessarily sustainable.

Thus, in order to achieve sustainable life forms, one has to find just the right combination of rules and starting conditions. Eventually, you get the sense that life in this little microcosm is quite fragile with respects the laws of its universe.

Ants, Brains and Cities

An analogous situation is found in many seemingly complex areas in nature. In his book entitled “Emergence: The connected lives of Ants, Brains and Cities“,  Steven Johnson shows how individual agents (like the cells in the Game of Life) who follow simple rules can collectively produce highly complex behaviour.

For example, neurons (brain cells) follow extremely simple rules: when a signal arrives from a connected cell, the cell performs a simple mathematical calculation to determine whether it should forward the signal to another connected cell, and if so to which cell. That is it. And from those very simple rules extremely complex behaviours arise, such as conscious thought, hypothetical thinking, and other marvels of human cognition.

The same emergence happens with ants. Each ant follows some very simple rules: when it meets another ant, they exchange some pheromones to let each other know what type of work they are doing. Then if an ant encounters too many other ants performing the same task as him, then he changes to something else. From these simple rules,  complex behaviour on the colony level emerges. It becomes self-sustaining, the colony collectively calculates the best location to store dead bodies and other waste away from primary food sources, duties are always balanced so as to always have just the right amount of food without waste piling up, and so on.

Whilst these emergent behaviours are incredible when compared with the simplicity of the rules followed by individual agents (be they blocks in the Game of Life, ants in a colony, or neurons in the brain), it should be noted that such behaviour would not exist if the rules were even slightly different, as we have seen was the case with the Game of Life. Thus, if the rules governing neuronal firing was different, or if the way ants decide to change roles was not exactly the same, then we would not have consciousness, and ants would not form successful colonies.

Lessons for our Macrocosm

When you think about the fragility of emergent systems in terms of our much more complex universe, some things become immediately apparent. Imagine the rules governing chemical reactions were slightly different, or if there was significantly less energy during the Big Bang, or if the speed of light was a bit slower or a bit faster. Just like in the Game of Life, such alterations to the rules or starting conditions would cause the emergent systems we see in our universe to not be possible.

This then leads to an interesting question: Why are the rules and starting conditions of our universe set in a way that allows for stars, life and human consciousness to all form? Now that is an interesting question…